Coupled Oscillators and the Tale of Huygen’s Clocks

First, watch this video.

That’s a little odd. Each of those metronomes is set to oscillate at exactly the same frequency, and they start out of phase with each other. How could they possibly finish up in perfect synchrony? Has some crazy scientist broken space-time so that our timepieces are no longer accurate?

Well that would certainly make getting to class on time more troublesome.

This isn’t the case of course. That would be almost too easy. Rather, this is an example of coupled oscillation.

Let’s wind the narrative clock back a few hundred years.

It’s February of 1665 and the great Dutch physicist Christian Huygens, inventor of the pendulum clock, is confined to his bed with a minor illness and nothing to do. His room is full of grand timepieces; ornate grandfather clocks, diminutive table-tickers and pristine cuckoo-clocks on the walls. Huygens notices a pair of pendulum clocks he recently constructed sitting on a shelf nearby. They’re behaving… oddly. The two pendulums are swinging in perfect synchrony.

Now, Huygens is a good clockmaker (although he’ll never say so himself) and he knows that his clocks aren’t so perfect as to be an exact measure of a second with every swing. No self-respecting scientist would allow such a mystery to pass them by. For the next few hours Huygens was unable to look away, and not once did the clocks break step with each other. He then tried knocking them out of sync. Within half an hour they were back to swinging in the same pattern. Somehow, the clocks were communicating.

What Huygens had discovered on his sick day off led to a whole new sub-branch of mathematics: the theory of coupled oscillators. The movements of the two pendulum clocks were translated through the shelf they were sitting on (much like the board in the video above) to form a coupled system. We can observe all sorts of weird behaviour in such systems, most commonly represented with weights on the end of springs.

Referring back to the video, a couple of things are clear.

The frequency of each metronome does not vary at any point.

Each metronome is identical (within statistical significance) in weight and structure to every other metronome.

Momentum is being transferred through the board, as indicated by its counter-movement with each swing.

So how do they synchronize with each other without changing frequency? Answer: The amplitude (distance swept out) of each swing gets either larger or smaller depending upon the motion of the board. You can see this if you observe the video closely around the 1:10 to 1:30 mark.

The implications of this field are more far-reaching than messing with timepieces however. Systems of coupled oscillation turn up in the mating flashes of fireflies along the tidal rivers of Malaysia, in the gait of a horse (trot, gallop or canter) and in your very own footsteps when walking next to someone on the way to 7-11. More importantly, they influence the mechanic behaviour of fluids and electromagnetic fields.

Sometimes it only takes the smallest of observations to make a big discovery.

One Response to “Coupled Oscillators and the Tale of Huygen’s Clocks”

This kind of scientific discovery is my favourite and it’s a shame most of them have already happened, the days of the lone polymath are dead. But more on topic, I really don’t have a cool question to ask I’m sorry, just commenting that these are the kinds of physics experiments I wish I’d done in school more often. Doesn’t require all the fancy maths to just have a look at it all.